%
% phasenraum.tex -- 
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math}
\begin{document}
\def\skala{1}
\begin{tikzpicture}[>=latex,thick,scale=\skala]

\def\m{1}
\def\K{0.444}

\pgfmathparse{sqrt(\K/\m)}
\xdef\o{\pgfmathresult}

\def\punkt#1#2{ ({#2*cos(#1)},{\o*#2*sin(#1)}) }

\foreach \r in {0.5,1,...,6}{
	\draw plot[domain=0:359,samples=360]
			({\r*cos(\x)},{\o*\r*sin(\x)}) -- cycle;
}

\def\tangente#1#2{
		\pgfmathparse{#2/\m}
		\xdef\u{\pgfmathresult}

		\pgfmathparse{-#1*\K}
		\xdef\v{\pgfmathresult}

		\pgfmathparse{sqrt(\u*\u+\v*\v)}
		\xdef\l{\pgfmathresult}

		\fill[color=blue] (#1,#2) circle[radius=0.03];
		\draw[color=blue,line width=0.5pt]
			({#1-0.2*\u/\l},{#2-0.2*\v/\l})
			--
			({#1+0.2*\u/\l},{#2+0.2*\v/\l});
}

\foreach \x in {-6.25,-5.75,...,6.3}{
	\foreach \y in {-4.25,-3.75,...,4.3}{
		\tangente{\x}{\y}
	}
}

%\foreach \x in {0.5,1,...,5.5,6}{
%	\tangente{\x}{0}
%	\tangente{-\x}{0}
%	\foreach \y in {0.5,1,...,4}{
%		\tangente{\x}{\y}
%		\tangente{-\x}{\y}
%		\tangente{\x}{-\y}
%		\tangente{-\x}{-\y}
%	}
%}
%\foreach \y in {0.5,1,...,4}{
%	\tangente{0}{\y}
%	\tangente{0}{-\y}
%}

\fill[color=white,opacity=0.7] \punkt{60}{4} rectangle \punkt{59}{5.8};
\fill[color=white,opacity=0.7] \punkt{0}{4} rectangle \punkt{18}{4.9};

\draw[->,color=red,line width=1.4pt]
	plot[domain=0:60,samples=360]
		({4*cos(\x)},{\o*4*sin(\x)});

\draw[->] (-6.5,0) -- (6.7,0) coordinate[label={$x$}];
\draw[->] (0,-4.5) -- (0,4.7) coordinate[label={right:$p$}];

\fill[color=red] \punkt{60}{4} circle[radius=0.08];
\node[color=red] at \punkt{60}{4} [above right]
	{$\begin{pmatrix}x(t)\\p(t)\end{pmatrix}$};

\fill[color=red] \punkt{0}{4} circle[radius=0.08];
\node[color=red] at \punkt{0}{4} [above right]
	{$\begin{pmatrix}x_0\\0\end{pmatrix}$};

\fill[color=white] (4,0) circle[radius=0.05];
\node at (3.9,0) [below right] {$x_0$};
\fill (0,{\o*4}) circle[radius=0.05];
\node at (0.1,{\o*4+0.05}) [below left] {$\omega x_0$};

\end{tikzpicture}
\end{document}